Mathematics — Old Questions (TPSC)
Q11. First Rs. 8,000 of annual income is tax free and income tax is 1 % beyond this. An employee paid Rs. 160 as income tax in a year. His monthly income is :
First Rs. 8,000 of annual income is tax free
Income tax rate beyond Rs. 8,000 = 1%
Given income tax paid in a year = Rs. 160
Let taxable income beyond Rs. 8,000 = x
Then,
1% of x = 160
x = 160 × 100 = 16,000
Total annual income =
Tax free income + Taxable income
= 8,000 + 16,000
= Rs. 24,000
Monthly income =
24,000 ÷ 12 = Rs. 2,000
Answer: The monthly income of the employee is Rs. 2,000.
📌 Exam tip: Always find taxable income first, then add tax-free income.
Q12. Two person start from the same point and walk on a circular path at the same speed but in opposite direction. They will be diametrically opposite to each other when each has covered :
Both persons start from the same point on a circular path
They walk at the same speed but in opposite directions
So, the distance between them increases at double speed
They will be diametrically opposite when the distance between them
equals half of the circumference of the circle
Hence, each person must cover:
Half of circumference ÷ 2 = 1 ÷ 4 of the circular path
Correct Option: (D) 1/4th distance
Exam Tip:
On a circular track, if two persons move at the same speed in opposite directions,
each must cover 1/4th of the track to be diametrically opposite.
Q13. If the radius of a circle is diminished by 10 % , then its area is diminished by :
Area of a circle = πr2
Let original radius = r
Radius is diminished by 10%
New radius = 90% of r = 0.9r
New area = π(0.9r)2
= π × 0.81r2
Original area = πr2
Decrease in area =
(πr2 − 0.81πr2)
= 0.19πr2
Percentage decrease in area = 19%
Answer: The area of the circle is diminished by 19%.
📌 Exam shortcut:
If radius changes by x%,
area changes by (2x − x²/100)%
Here → 2(10) − 1 = 19%
Q14. The value of √156 . 25
Given expression = √156.25
Write 156.25 as a fraction:
156.25 = 15625 ÷ 100
So,
√156.25 = √(15625 ÷ 100)
= √15625 ÷ √100
√15625 = 125
√100 = 10
Therefore,
√156.25 = 125 ÷ 10 = 12.5
Answer: The value of √156.25 is 12.5.
📌 Exam tip:
For square roots of decimals, convert into fractions first—calculation becomes easy and accurate.
Q15. What is 50 % of 40 % of Rs. 3,450 ?
We have to find 50% of 40% of Rs. 3,450
First find 40% of Rs. 3,450:
40% of 3450 = (40 ÷ 100) × 3450 = 1380
Now find 50% of 1380:
50% of 1380 = (50 ÷ 100) × 1380 = 690
Answer: 50% of 40% of Rs. 3,450 is Rs. 690.
📌 Exam tip:
When multiple percentages are involved, apply them step by step or multiply their decimal forms directly.
Q16. If a : b = 4 : 5 and b : c = 6 : 7, then a : c will be equal to :
Q17. A student was asked to add 16 and subtract 10 from a number. He by mistake added 10 and subtracted 16. if his answer is 14, what is the correct answer ?
Q18. A train crosses a pole in 15 seconds, while it crosses 100 metre long platform in 25 seconds. The length of the train is :
Q19. One-Fourth percent of 18 is :
One-fourth percent = 1 ÷ 4 % = 0.25%
0.25% of 18 = (0.25 ÷ 100) × 18
= 0.045
Answer: One-fourth percent of 18 is 0.045.
📌 Exam tip:
To find a fraction of a percent, convert it into decimal first, then multiply.
Q20. A sum of Rs. 427 is to be divided among A, B and C in such a way that 3 times A's share, 4 times B's share and 7 times C's share are all equal. The share of C is then :
Given that,
3 times A's share = 4 times B's share = 7 times C's share
Let the common value be x
So,
A's share = x ÷ 3
B's share = x ÷ 4
C's share = x ÷ 7
Total sum = 427
So,
(x ÷ 3) + (x ÷ 4) + (x ÷ 7) = 427
Taking LCM of 3, 4 and 7 = 84
(28x + 21x + 12x) ÷ 84 = 427
61x ÷ 84 = 427
61x = 427 × 84
x = (427 × 84) ÷ 61
x = 588
C's share = x ÷ 7
= 588 ÷ 7
= 84
Answer: The share of C is Rs. 84.
📌 Exam tip: When multiples of shares are equal, express each share in terms of a common variable first, then form the total-sum equation.